29 citations · 159 across the 40 of their papers we have counts for
6 papers · 1 filter
Symmetric Schroder paths and restricted involutions
Eva Y. P. Deng, Mark Dukes, Toufik Mansour +1
Let be the set of permutations in the symmetric group with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns . We prese…
Smooth words and Chebyshev polynomials
Arnold Knopfmacher, Toufik Mansour, Augustine Munagi +1
A word over the alphabet is said to be {\em smooth} if there are no two adjacent letters with difference greater than 1. A word is said to be…
On the number of combinations without certain separations
Toufik Mansour, Yidong Sun
In this paper we enumerate the number of ways of selecting objects from objects arrayed in a line such that no two selected ones are separated by object…
Identities involving Narayana polynomials and Catalan numbers
Toufik Mansour, Yidong Sun
We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the N…
Bell Polynomials and -generalized Dyck Paths
Toufik Mansour, Yidong Sun
A {\em k-generalized Dyck path} of length is a lattice path from to in the plane integer lattice consisting of horizontal-steps $(k…
Separable d-permutations and guillotine partitions
Andrei Asinowski, Toufik Mansour
We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula and explicit formula. W…